Wideband, solid-state driven RF systems for PSB and PS longitudinal damper. M.Paoluzzi BE/RF 9 September 2014

Summary Configuration and limits Amplifier topology RF Currents and amplifier in the PSB RF Currents and amplifier in the PS Damper

Configuration and limits At low and mid frequency, stacking more cores across a gap linearly adds up the core impedances. At high frequency the response is mainly limited by the structure capacitance that becomes effective earlier. Full exploitation of wideband characteristics when using a single core on each side of the gap. Core dimensions dictated by PSB limitation 330/200/25 mm, indirect cooling. 750 W Water Tin=18 ˚C Water Tout=33 ˚C Flow = 3 litres/min Assuming a maximum temperature of 100°C and a reasonable duty cycle each ring can dissipate 1 kW. Power compatible with compact solid state amplifier. 2 rings 800Vpk above 400 kHz

Amplifier topology Space available for the amplifier limited in the PSB. In the available volume 16 200W power stages, combiner, driver and ancillaries could be stacked. Power stages connectable as: Single ended amp (16 to 1 combiner 3kW) two amps per gap. Push Pull amp (2x 8 to 1 combiner 2x1.5kW) one amp per gap. Input circuit with paralleled gates and driven by a high impedance stage (differential capacitive input for FB). Important parameter : N number of 200 W modules n voltage transformation ratio drain to out. Differential output : N=8, n=12   Single ended output : N=16, n=16

RF Currents With narrowband ferrite loaded cavities the beam-cavity interaction is mainly limited to the harmonic component at cavity resonance. The wideband response of the Finemet® loaded cells requires acting on more harmonics. Assuming the gap impedance to be purely resistive (Rgap), frequency independent and driven by the generator and beam currents , to obtain the gap current: IGap=VGap/Rgap the generator must supply: This simple relation can be applied to compute the generator current required for acceleration by setting VGap at the fundamental frequency at the required value. It can also be used for computing what’s needed for cancelling the higher harmonic components zeroing the corresponding VGap.

MOSFETs’ saturation currents: Currents in the PSB Assume the acceleration cycles shown below and system composed of 12 accelerating cells (700Vpk each). Maximum current is required around 1.74 MHz Stable phase 45 and 50 degrees for 1.4 1013 and 2.5 1013 protons respectively. The right hand side plots show the computed shapes of the beam and generator currents. The maximum required generator currents are 16 A and 26 A. With ID/IB = 1.5 the Push-Pull amplifier version can be used. MOSFETs’ saturation currents: Green VRF151 Violet SD2942 Blue MRF151 Red MRFE6VP6300

System with push pull amplifier Amplifier for PSB Feedback loop gain =10dB System with push pull amplifier

Currents in the PS damper 2012 LIU Parameters Beam type LHC25ns LHC50ns TOF Fixed target Damper Active Inactive Possibly active Beam intensity 1.28 1013 ppp 1.92 1013 ppp 1.48 1013 ppp 1.0 1013 ppp up to 4 1013 ppp DC current 1.0 A 1.5 A 1.16 A 0.8 A 3.2 A Current per spectral component, short bunch approximation 2 A 3 A 2.32 A 1.6 A 6.4 A Peak current at transition 10.2 A 15.5 A 11.9 A 50 A 25 A Bunch length 18 ns 40 ns 20 ns Intensity per bunch at extraction 2.7 1011 ppb 4.2 1011 ppb coasting beam Peak current at extraction 17.3 A 26.8 A 100 A 4 ns Duration of peak ~0.3 ms ~ 1ms To produce the required 5 kV maximum voltage a six-cell system is used for the PS Damper. A consistent part of the required RF current and power will be used for wake field cancellation. Radiation issues impose the amplifier installation at some distance for the cavities (No FB possible). The single ended amplifier solution gives more reserve. MOSFETs’ saturation currents: Green VRF151 Violet SD2942 Blue MRF151 Red MRFE6VP6300

Amplifier for the PS Damper System with single ended amplifier